The ability to inhibit ongoing responses that suddenly become inappropriate is essential for safe and effective interaction with an ever-changing and unpredictable world. Response inhibition is quantified by the unobservablestop-signal reaction time (SSRT), the completion time of an inhibitory process triggered by a signal to stop responding. SSRTs can be inferred based on a model in which inhibitory and response processes race with each other to control behavior. Inhibition is usually studied in the context of choice responses, but there has been increasing interest in what is often a key component of skilled behavior, stopping a response that is timed to coincide with an anticipated event. We show that SSRT measurement via the standard race model fails for anticipated responses because the stop signal changes the perception of the passage of time, due to the long-known “filled-interval illusion”. We propose a computational model of anticipated response inhibitionthat takes account of this distortion of time perception and show that this model produces valid estimates of not only SSRT, but also another key process that determines inhibitory ability, lapses in attention. Our new modeland accompanying Bayesian estimation procedures provide a solid basis for the burgeoning study of timed-action control.